Problem: Solve for $x$ and $y$ using substitution. ${2x+5y = -4}$ ${y = -4x+10}$
Answer: Since $y$ has already been solved for, substitute $-4x+10$ for $y$ in the first equation. ${2x + 5}{(-4x+10)}{= -4}$ Simplify and solve for $x$ $2x-20x + 50 = -4$ $-18x+50 = -4$ $-18x+50{-50} = -4{-50}$ $-18x = -54$ $\dfrac{-18x}{{-18}} = \dfrac{-54}{{-18}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -4x+10}\thinspace$ to find $y$ ${y = -4}{(3)}{ + 10}$ $y = -12 + 10$ $y = -2$ You can also plug ${x = 3}$ into $\thinspace {2x+5y = -4}\thinspace$ and get the same answer for $y$ : ${2}{(3)}{ + 5y = -4}$ ${y = -2}$